Generalized Hamel basis and basis extension in convex cones and uniquely divisible semigroups

In the work, a concept of sublinear independence in an arbitrary convex cone is introduced and the corresponding generalization of Hamel basis is studied. Applying these results to the cones generated by uniquely divisible semigroups ((UD)-semigroups) allows us to extend obtained results for the class of (UD)-semigroups. Some applications are considered.